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A352740 Irregular table T(n, k) read by rows; the n-th row contains, in ascending order, the numbers k < n such that for any base b >= 2, the sum of digits of n and k in base b are different.

%I A352740 #9 Apr 01 2022 09:03:48
%S A352740 0,0,0,2,0,3,0,4,0,0,4,6,0,6,7,0,7,8,0,8,0,6,8,9,10,0,11,0,12,0,10,12,
%T A352740 0,8,12,14,0,13,15,0,14,15,16,0,15,16,0,16,17,18,0,19,0,20,0,0,12,16,
%U A352740 18,20,21,22,0,23,0,24,0,18,24,0,14,21,24,25,26
%N A352740 Irregular table T(n, k) read by rows; the n-th row contains, in ascending order, the numbers k < n such that for any base b >= 2, the sum of digits of n and k in base b are different.
%C A352740 A352671 gives row lengths.
%H A352740 Rémy Sigrist, <a href="/A352740/b352740.txt">Table of n, a(n) for n = 1..10302</a> (rows for n = 1..2000, flattened)
%H A352740 Rémy Sigrist, <a href="/A352671/a352671.png">Scatterplot of (x, y) such that x, y <= 1000 and for any base b >= 2, the sum of digits of x and y in base b are different</a>
%F A352740 T(n, 1) = 0.
%e A352740 irregular table begins:
%e A352740      1:    [0]
%e A352740      2:    [0]
%e A352740      3:    [0, 2]
%e A352740      4:    [0, 3]
%e A352740      5:    [0, 4]
%e A352740      6:    [0]
%e A352740      7:    [0, 4, 6]
%e A352740      8:    [0, 6, 7]
%e A352740      9:    [0, 7, 8]
%e A352740     10:    [0, 8]
%o A352740 (PARI) row(n) = { my (v=[]); for (k=0, n-1, my (ok=1); for (b=2, max(2, n+1), if (sumdigits(n, b)==sumdigits(k, b), ok=0; break)); if (ok, v=concat(v,k))); v }
%Y A352740 Cf. A216789, A352671 (row lengths).
%K A352740 nonn,base,tabf
%O A352740 1,4
%A A352740 _Rémy Sigrist_, Mar 31 2022